Final answer:
There are 38,760 different ways that the top 6 finishers out of 20 can advance to the finals, calculated by using the combinations formula C(20, 6).
Step-by-step explanation:
The question deals with finding out in how many different ways the top 6 finishers out of a group of 20 can advance to the finals. This is a problem of combinations since the order of finishers does not matter, only who is in the top 6. The formula for combinations is given as C(n, k) = n! / (k! * (n - k)!), where n is the total number of items, and k is the number of items to choose.
To calculate the number of ways the top 6 can advance, we use the combination formula with n = 20 and k = 6
C(20, 6) = 20! / (6! * (20 - 6)!) = 20! / (6! * 14!) = 38760.
Therefore, there are 38,760 different ways in which the top 6 finishers out of 20 can advance to the finals.